One albino laboratory rat is an independent variable.
To investigate how alcohol affects reaction times, sixty participants were randomly split into two groups. Those in one group drank a certain amount of alcohol, while those in the other group drank non-alcoholic beverages. Both groups' reaction times were timed before and after the beverage.
A variable that is independent is one that is capable of standing alone.The independent variable is unaffected by other variables and remains unchanged at all times.Although the other elements may be out of the ordinary, it still stands on their own.A person's age, for instance, is an independent variable.Know more about reaction time
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The question is incomplete and wrong:
Sixty albino laboratory rats were randomly divided into two groups as part of a study on the effects of alcohol on reaction time. Each member of one group consumed a specified amount of alcohol and members of the other group had a non-alcoholic beverage. The reaction time of both groups was measured before and after taking the beverage/alcoholic drink. What is the INDEPENDENT VARIABLE?
a. Amount of alcohol
b. Reaction time
c. One albino laboratory rat
d. Sixty albino laboratory rats
The weights (in pounds) of the players on a professional basketball team by position are as follows.
Power forwards: 235, 255, 295, 245; small forwards: 235, 235; centers: 255, 245, 325; point guards: 205, 185, 205; shooting guards: 205, 215, 185.
Make a graph that represents the weights and positions of the players. Does there appear to be a correlation between the body weights and the positions of players in professional basketball? Explain your reasoning
Answer:the frist one
Step-by-step explanation:
How do you find the measure of each acute angle in a triangle?
Place your protractor on a straight line to measure the acute angle. Line up the horizontal line on the baseline of your protractor, placing the centre of your protractor over the vertex. Examine where the diagonal line crosses the protractor to specify the number of degrees in the acute angle.
Measuring angles is a significant topic in geometry. An angle can be measured by operating a protractor, precisely. An angle is measured in degrees, hence it's called ‘degree measure’.
One complete revolution is equivalent to 360 degrees, hence it is divided into 360 parts. Each part of the one complete revolution is a degree. If we know how to measure angles, then it will be very easy to construct an angle using a protractor.
Any angle whether it is an obtuse, acute, right or reflex angle, can be calculated using a protractor. Although we are able to differentiate between acute, obtuse or reflex angles, based on the right angle.
If we have two acute angles to calculate, then we cannot calculate the greater angle among the two. Thus, we have to use a protractor to measure the angles accurately.
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A matrix a is given. Determine if the system ax = b (where x and b have the appropriate number of components) has a solution for all choices of b.
If the rank of matrix A is equal to the number of columns of A, and the rank of matrix A is equal to the rank of the augmented matrix [A|b], then the system Ax = b will have a unique solution for all choices of b. Otherwise, the system Ax = b will not have a unique solution for all choices of b.
To determine if the system ax = b has a solution for all choices of b, we need to look at the rank of the matrix A and the rank of the matrix formed by appending the vector b to the matrix A.
The rank of a matrix is the number of linearly independent rows or columns in the matrix. If the rank of matrix A is equal to the number of columns in A, then matrix A is full rank and the system Ax = b will have a unique solution for all choices of b. If the rank of matrix A is less than the number of columns in A, then matrix A is not full rank, and the system Ax = b will not have a unique solution for all choices of b.
If the rank of matrix A is equal to the rank of the matrix formed by appending the vector b to matrix A, the system Ax = b will have a unique solution for all choices of b. If the rank of matrix A is less than the rank of the matrix formed by appending the vector b to matrix A, the system Ax = b will not have a unique solution for all choices of b.
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i deposit 2000 in an account that earns 5% simple interest how much is the investment worth after 8 years
After 8years the investment will have worth 2800
What is simple interest?Simple interest is the interest amount for a particular principal amount of money at some rate of interest. In contrast, compound interest is the interest calculated on the principal and the interest accumulated over the previous period.
Simple interest is given as:
I = (P×R×T)/100
where P = principal
R = rate of the interest
T = time for the loan / savings
therefore I = 2000× 5× 8/100
I = 800
Therefore that amount realized after 8years
= 2000+800 = 2800
therefore the investment will worth 2800 after 8 years.
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(2r⁹) (8r⁴)
_______ = ?
4r⁶
please hurry
Answer:
=4r⁷
Step-by-step explanation:
(2r⁹) (8r⁴)
=_____
4r⁶
16r¹³
=______
4r⁶
=16r¹³ ÷ 4r⁶
=4r⁷.
Answer: 4r⁷
Step-by-step explanation: (2r⁹) (8r⁴) = _____ 4r⁶ 16r¹³ = ______ 4r⁶ 16r¹³ ÷ 4r⁶ 4r⁷
Eric had a balance of $4 in his savings account after making a deposit he has $25 in his account what is the overall change in his account?
Answer:
21 dollars is the change.
Step-by-step explanation:
If u do division 25/4 its equals to 5.25 which could be the answer too.
3. For each quadratic equation, identify a, b, and c. State whether the vertex point will be a
maximum point or a minimum point.
Quadratic equation
y = 3x²-3x + 5
y = -2x² + x
y = 1/2x² + 6
y=-3x² + 1/2x - 2
y=x²-2x+6
a
b
C
max/min
For each quadratic equation, the value of a, b and c are mentioned below. Also maximum or minimum points are mentioned here.
What is quadratic equation?A variable with the largest power of two in a quadratic equation is called a variable. Quad, which signifies square, is the root of the term quadratic. The phrase must be two times its own strength, neither higher nor lower.
Given that they are the x values for which f(x) = 0, the roots of the function f(x) = ax² + bx + c correspond to the solutions of the quadratic equation ax² + bx + c = 0.
The term ax² is known as the quadratic term (hence the function's name), the word bx is known as the linear term, and the value c is known as the constant term.
a. y = 3x²-3x + 5, comparing this with general quadratic equation ax² + bx + c and get a = 3 and b = -3 and c = 5
thus x = - (b/2a)
x = - (-3/6)
x = -1/2
as a > 0 thus the equation has the minimum value and that is:
y = 3(-1/2)² -3(-1/2) + 5
y = 3/4 + 3/2 + 5
y = 13/2
b. y = -2x² + x comparing this with general quadratic equation ax² + bx + c and get a = -2 and b = 1 and c = 0
thus x = - (b/2a)
x = - (1/-4)
x = 1/4
as a < 0 thus the equation has the maximum value and that is:
y = -2(1/4)² + (1/2)
y = -1/8 + 1/2
y = 3/8
c. y = 1/2x² + 6 comparing this with general quadratic equation ax² + bx + c and get a = 1/2, b = 0 and c = 6
thus x = - (b/2a)
x = - (1/2×0)
x = 0
as a > 0 thus the equation has the minimum value and that is:
y = 1/2(0)² + 6
y = 6
d. y=-3x² + 1/2x - 2 comparing this with general quadratic equation ax² + bx + c and get a = -3, b = 1/2 and c = -2
thus x = - (b/2a)
x = - [(1/2)/-6]
x = 1/12
as a < 0 thus the equation has the maximum value and that is:
y=-3(1/12)² + 1/2 (1/12) - 2
y = - 1/48 + 1/24 - 2
y = -45/48
e. y=x²-2x+6 comparing this with general quadratic equation ax² + bx + c and get a = 1, b = -2 and c = 6
thus x = - (b/2a)
x = - (-2/2)
x = 1
as a > 0 thus the equation has the minimum value and that is:
y=(1)²-2(1)+6
y = 5
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1.
Evaluate the following expression: 5/7 to the power of 2
To evaluate an algebraic expression is to determine its value when a certain number is used in place of the variable. Therefore the correct option is 25/49
In order to evaluate an expression, we first swap out the variable for the given number, and then we use the order of operations to simplify the expression.To "critically evaluate," you must express your judgment regarding the validity of a claim or body of research findings. This needs to be done with the utmost seriousness. Specify the degree to which a claim or research finding is true in your opinion.To evaluate the expression of 5/7 to the power of 2 we will-
[tex]5/7² = 5/7 X 5/7 = 25/49[/tex]
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Find the values of x and y given
Answer: x = 32 & y = 51
Step-by-step explanation:
Since
ΔMNP ≅ ΔTUS
Therefore
NP ≅ US
2x - y = 13
y = 2x - 13 __eq_1
Since
ΔMNP ≅ ΔTUS
therefore
∠N ≅ ∠U
so, if we find ∠N we'll be able to find ∠U as well
since the sum of angles of a triangle is 180, therefore
∠N = 180 - (∠M + ∠P )
∠N = 180 - (142 + 24)
∠N = 14°
we know ∠N ≅ ∠U
therefore
14 = 2x - 50
2x = 64
x = 64÷2
x = 32 __eq_2
putting eq_2 in eq_1
y =
2x - 13
y = 2 (32) - 13
y = 51 __eq_3
x = 32 & y = 51 ...Answer
hope that helps...
A store is having a 10% sale on all items. There is an additional $30 discount to the sale price of any bicycle. Let x represent the price in dollars, and let f(x) = x − 30 and g(x) = x − 0. 10x = 0. 90x represent the discounts. Which function can the store manager use to find the final price of a bicycle? Group of answer choices f+g g∘f g−f f∘g
The store manager can use f∘g function to find the final price of a bicycle.
Let the buying price be Y,
Store is offering sale on the item given by function,
f(x) = x - 30
And offering an additional discount given by function,
g(x) = x - 0.1x = 0.9x
So final price be written as;
0.9x - 30 [ 10% off and 30$ discount ]
Then 0.9x - 30 = f∘g ( operations of functions of functions ).
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
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In a survey of women in a certain country (ages 20 - 29), the mean height was 63.2 inches with a standard deviation of 2.67 inches. Answer the following questions about the specified normal distribution.
What height represents the 95th percentile?
What height represents the first quartile?
If in a survey of women in a certain country (ages 20 - 29), the mean height was 63.2 inches with a standard deviation of 2.67 inches.
a. The height that represents the 95th percentile is 67.61.
b. The height that represents the first quartile is 61.4.
How to find the 95th percentile and first quartile?Mean (μ) = 63.2
Standard deviation (σ) = 2.67
a. The value of the 95th percentile
Value of the 95th percentile = 63.2 + 1.65(2.67)
Value of the 95th percentile = 63.2 + 4.4055
Value of the 95th percentile = 67.61
b. value of the first quartile (25th percentile)
Value of the first quartile = 63.2 + (-0.67) (2.67)
Value of the first quartile = 63.2 + (-1.7889)
Value of the first quartile = 61.4
Therefore the height that represents the 95th percentile is 67.61 and the height that represents the first quartile is 61.4.
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Give three expressions equivalent to (2³)^5x
Expressions that perform similarly but differ in appearance are said to be equivalent expressions. When the same value(s) for the variable are entered, two algebraic expressions that are equivalent will have the same value (s).
What is an Algebraic Expression?An algebraic expression is a mathematical expression made up of variables, coefficients, constants, and operations including addition, subtraction, multiplication, and division. In most cases, something is said to be equivalent if two of them are the same.
Similar to this, analogous expressions in mathematics are those that, despite their differences in appearance, have the same meaning.
The two expressions, however, produce the identical outcome when the values are inserted into them.
Example
If the provided expression has an equivalent, write it down: 3x+9
Solution:
expressed in this way: 3x+9
The analogous equation is equal to the expression when 3 is removed from it, which is = 3(x+3).
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Classifying Consistent Dependent, Consistent Independent & Inconsistent Systems of Linear Equations Example 1
Choose the correct classification of the system of linear equations shown in the graph.
a. Consistent Dependent
b. Consistent Independent
c. Inconsistent
d. None of the above.
A system of linear equations can be classified into 3 different ways based on their nature of roots and their graphical representation.
Step 1: Examine the given graph.
Step 2: Determine if the lines cross exactly once, are exactly the same, or are parallel to each other.
Step 3: Classify the system of linear equations as consistent dependent, consistent independent, or inconsistent based on your findings in step 2.
A system of linear equations is consistent dependent if it has an infinite number of solutions i.e the graphs of the lines in the system are the same, it is consistent independent when it has exactly one solution i.e the graphs of the lines in the system cross exactly once and a system is inconsistent if it has no solutions i.e the graphs of the lines do not intersect and they are parallel.
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Can someone help md with my slope maze
What is substitution formula?
There is no particular formula for substitution instead it is a method to solve the linear equations in two variables.
The substitution method is a simple method to solve a system of linear equations algebraically and find the solutions of the variables. As the name implies, it applies to finding the value of the x-variable in terms of the y-variable from the first equation and then substituting the value of the x-variable in the second equation.
In this method, we can find the value of the y-variable by solving the equation. And then, we can substitute the value of y in any of the given equations to find the value of x.
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Lola says these two expressions have the same value.
Expression A
Expression B
Left-bracket (StartFraction a Over b EndFraction) Superscript negative 4 Baseline Right-bracket Superscript 0
Left-bracket (StartFraction a Over b EndFraction) Superscript 0 Baseline Right-bracket Superscript negative 4
Which explains whether Lola is correct?
Lola is correct because each expression has a value of 1. Option A is correct.
What is the expression?The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial expression.
here,
Given expression
A = [tex][[a /b]^{-4}]^0[/tex]
B = [tex][[a /b]^{0}]^{-4}[/tex]
Since we know that,
a⁰ = 1
So,
A = [1]
B = 1⁻⁴ = 1
Thus, Lola is correct because each expression has a value of 1. Option A is correct.
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help please last one promise
Answer:
2y-7=5
Step-by-step explanation:
since the number represents y
the product of 2 and a number would be 2y
then since it says seven less than that you subtract 7 from 2y
this gives you 2y-7
finally, it says its equal to 5
so then all you have to put is 2y-7=5 as your answer since it only asks you to make the equation based off the sentence, not solve it.
What is inverse of a number?
The inverse of a number is it's reciprocal. Consider a number y where y is not equal to zero. Then the inverse of y is the reciprocal of the y that is 1/y.
The inverse is a function or an operation which reverses the order of operation of another function or an operation”.
For example, Calculate the inverse of a number 5, 15, 35 and 46.
To find out the inverse of a number, we have to take the reciprocal of the given numbers.
So, the inverse of the number 5 will be 1/5.
The inverse of the number 15 will be 1/15.
The inverse of the number 35 will be 1/35.
The inverse of the number 46 will be 1/46.
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27⅔ multiply by 32 minus 2 over 5 divided by 64 raised to the power of 5 over 6
Using BODMAS, the answer of the given question is 13232 / 15.
What is the math rule of BODMAS?The brackets must be solved first, then powers or roots (i.e. of), Division, Multiplication, Addition, and finally Subtraction, according to BODMAS rule. Any expression can only be solved correctly if the BODMAS rule or the PEDMAS rule are applied.
The other operations must be solved in the same order. Brackets (B) are followed by the order of powers or roots, which is then followed by multiplication, addition, subtraction, and finally division.
According to the question,
[tex]27 \frac{2}{3} \times 32 - \frac{2}{5} \div 64^{\frac{5}{6} }[/tex]
Using BODMAS,
⇒ 83/3 × 32 - [tex]\frac{2}{5}[/tex] ÷ [tex]64^{\frac{5}{6} }[/tex]
⇒ 83/3 × 32 - 2/5 ÷ [tex](2^{6})^{\frac{5}{6} }[/tex]
⇒ 83/3 × 32 - 2/5 ÷ 2⁵
⇒ 83/3 × 32 - 2/5 × 1/2⁵
⇒ 83/3 × 32 - 2⁴/5
⇒ 2656 / 3 - 2⁴/5
⇒ 2656 / 3 - 16/5
⇒ 13280 - 48 / 15
⇒ 13232 / 15
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What is the answer to 2.5 4k 2 )= 12k?
Answer: k = 5/2 = 2.500
Step-by-step explanation: k=25=221=2.5
Which has the greater value, |4.2| or |3.6|?
Answer:
4.2 has a greater value
since 4.2 is greater than 3.6
Step-by-step explanation:
Since neither numbers are negative, the absolute value around the numbers do not change the values. So nothing changes and we know 4.2 is greater than 3.6
What is the equation for no solution?
The required equations are y = 3x + 2, y = 3x + 5 which have no solution.
What is equation of line?The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.
According to question:For no solution of equation,
equation of line must be parallel and for parallel line, Slope should be same.
Or we can say There won't be a solution if (a1/a2) = (b1/b2) (c1/c2). An inconsistent pair of linear equations is the name given to this kind of equation.
y = 3x + 2
y = 3x + 5
Thus, required two equation are y = 3x + 2, y = 3x + 5 which have no solution.
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What is the measure of angle ABE?
The measure of angle ABE is ___degrees
The measure of angle ABE is 40 degrees.
What is angle ?The angle formed by two rays is in the plane containing the rays.An angle is also formed by the intersection of two planes.An angle is a combination of two rays (half rays) that have a common endpoint.The latter is known as the apex of the angle and the ray is known as the side.There are also cases of angled legs and arms.In plane geometry, the figure formed by two rays or lines that share a common endpoint is called an angle.The word "angle" comes from the Latin word "angulus" which means "horn".When two lines intersect each other, the vertically opposite angles are equal.
Therefore, angle ABE = angle CBD
angle ABE = 40 degrees.
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At a recent cross country meet, spectators had to pay to get in. It cost $7 for adults and $3 for
students. The Booster Club selling tickets forgot to keep track of how many adult and student
tickets they sold. However, they did know they sold 155 total tickets and made $645
The Booster Club sold 45 tickets to the adults and 110 tickets to the students.
In the given question, the Booster Club selling tickets wants to keep track of how many adult and student tickets they sold.
At a recent cross country meet, spectators had to pay to get in.
It cost $7 for adults and $3 for students.
However, they did know they sold 155 total tickets and made $645.
Let total x tickets sold to adults.
Let total y tickets sold to students.
They sold total 155 tickets. So the required equation is:
x + y = 155...(1)
The cost of one adult ticket is $7. So the cost of x tickets are 7x.
The cost of one student ticket is $3. So the cost of y tickets are 3y.
They earned total $645. So the required equation is:
7x + 3y = 645...(2)
Now solving the both equation using the elimination method
Multiply the equation 1 by 3 and then subtract by equation 2, we get
7x + 3y - (3x + 3y) = 645 - 465
After solving, we get
4x = 180
Divide by 4 on both side, we get
x = 45
Now putting the value of x in equation 1, we get
45 + y = 155
Subtract 45 on both side, we get
y = 110
Hence, the Booster Club sold 45 tickets to the adults and 110 tickets to the students.
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Need to know if x is greater than or less than the solution and why
The definition of an equation is an algebraic expression that often connects unknown variables to known variables or constants.
What is the solution of an expression?A general rule is that the algebraic expression should take any of the following forms: addition, subtraction, multiplication, and division. Bring the variable to the left side and the other values to the right side in order to find the value of x. To determine the answer, simplify the values.
Equations are mathematical expressions that often connect unknown variables to known variables or constants. For instance, x + 2 = 15 and y2 = 4 are both equations. An equation's solution, also known as its root, is any value or group of values that may be used to transform the equation into a true statement.
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Gary rode his bike for 1 2/3 miles on Wednesday. On Thursday, he biked 5 times as far as on Wednesday. How many miles did Gary bike on Thursday?
Write your answer as a fraction or as a whole or mixed number.
Answer:
8.3 miles
Step-by-step explanation:
1 2/3 times 5= 8.3. He rode 8.3 miles
problem: report error a sphere is inscribed in a cube that has a surface area of square meters. a second cube is then inscribed within the sphere. what is the volume in cubic meters of the inner cube?
Total Surface area of the inner cube = 6 * 2 = 12 m²
Take a vertical cross-section through the center of the arrangement as shown in the following figure —
The surface area of the outer cube is 24 m²
Therefore, each face of this cube equals 4 m²
=> Each edge of the larger cube is two meters
The inner sphere's diameter is 2 meters since it meets the surface of the outer cube.
Thus, the sphere's radius (Viz OR) is equal to 1 m.
Taking into account Right Triangle OQR, QR = √ [ 1² + 1² ] = √2 m
=> The smaller cube's face area is equal to 2 m².
The inner cube's total surface area is equal to 6 * 2 = 12 m²
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The full question:
A sphere is inscribed in a cube that has a surface area of 24 m2. A second cube is then inscribed within the sphere. What is the surface area of the inner cube?
A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table.
Labor-Hours per Ski
Department
Fabricating
Finishing
Trick Ski
6
1
Slalom Ski
4
1
Maximum Labor-Hours
Available per Day
216
48
If the profit on a trick ski is $30 and the profit on a slalom ski is $40, how many of each type of ski should be manufactured each day to realize a maximum profit? What is the
maximum profit?
The maximum profit is S The maximum occurs when trick skis and slalom skis are produced.
If x is the quantity of trick skis sold and y is the quantity of slalom skis sold, and x and y are both nonnegative numbers, then x 0 and y 0.
A manufacturing company makes two types of water skis, a trick ski and a slalom ski?We can see from the first row of the table that 6x + 4Y 216 because 6x indicates the work hours required to make x number of trick skis and 4y is required to make y number of slalom skis. We get at 6X + 4Y 216 since the sum (6x+4y) cannot be greater than 216 hours.
Using a similar logic, the second row provides us with the following inequality:
X + Y ≤ 40
X 0 Y 0 6 X + 4 Y 216 X + Y 40
The points at the vertices are:
A = (0, 0)\sB = (0, 40)\sC = (12, 28)\sD = (33, 0) (33, 0)
By intersecting the border lines, one can locate each vertex point. For instance, the intersection of the boundary lines 6x+4y = 216 and x + y = 40 is point C.
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Evaluate the function requested. Write your answer as a fraction in lowest terms.
Triangle A B C. Angle C is 90 degrees. Hypotenuse A B is 25, Adjacent A C is 15, Opposite C B is 20.
Find sin A.
a.
sine A = four-fifths
c.
sine A = three-fifths
b.
sine A = four-thirds
d.
sine A = five-fourths
see picture.......
Examining the right triangle figure attached the value of sin A is
a. sine A = four-fifthsHow to get the value of sin AThe trigonometry sin A is worked using the pneumonic SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
Information from the question, viewing from angle A
opposite = 20
adjacent = 15
hypotenuse = 25
The value of sin A is calculated using sin, SOH
et the angle be x
sin x = Opposite / hypotenuse
sin x = 20 / 25
sin x = 4 / 5
sin x is 4/5
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5x+4y= -3 can u help me answer this pls
Answer: x=3-4y
_____
5
Step-by-step explanation: